Core and strongly core orthogonal elements in rings with involution

In this paper, we present a new concept of the core orthogonality for two core invertible elements a and b in rings with involution. a is said to be core orthogonal to b, if a#b = 0 and ba# = 0, where a # is the core inverse of a. The characterizations of the core orthogonality and the core additivity are provided. By using the matrix representations of the core orthogonal elements, the connection between the core orthogonality and the core partial order is also given. Moreover, the strongly core orthogonality is defined and characterized.